Achievement

The nature
of the pairing interaction that mediates superconductivity in the
two-dimensional Hubbard model has been addressed numerically in a
user project at the Center for Nanophase Materials Sciences. The
Hubbard model exhibits several phenomena remarkably similar to what
is observed in the cuprate high-temperature superconductors, including
superconductivity, antiferromangetism, and the nano-meter scale phase
separation present in some underdoped compounds. In this work a combination
of numerical dynamic cluster quantum Monte Carlo simulations and
diagrammatic techniques revealed the structure and nature of the
pairing interaction responsible for superconductivity. This work
established that the pairing interaction increases with momentum
transfer and decreases when the energy transfer exceeds a scale associated
with the antiferromagnetic spin susceptibility. This implies that
the pairing interaction is attractive between singlets formed on
nearest neighbor sites and that its dynamics is associated with the
antiferromagnetic spin fluctuation spectrum. The strength of the
pairing interaction is found to peak when the Coulomb repulsion is
of the order of the bandwidth, and increases as the system is underdoped.
An exact decomposition of the pairing interaction reveals that it
is mediated by the exchange of antiferromagnetic spin fluctuations
(see attached).

Significance

The relevant
parameter region of the Hubbard model to describe the cuprate superconductors
is at the crossover region between weak and strong electronic correlations.
This makes the study of this model extremely challenging since conventional
perturbative approaches fail. Employing a state-of-the-art many-body
technique, this work was able to address this region in a controlled
way for the first time. This work established that the pairing interaction
in the Hubbard model is of magnetic origin. The full characterization
of the nature of the pairing interaction is an important step towards
the design of materials that become superconducting at even higher
temperatures, enabling breakthroughs in real world applications that
will benefit from near-ideal conduction of electricity. Moreover,
the general concepts developed in this work provide a useful, unbiased
method for determining the nature of the leading correlations in
interacting many-electron systems and the character of the mechanism
responsible for them.

ORNL Research
by Thomas A. Maier. Co-authors were Douglas J. Scalapino from the
University of California, Santa Barbara and Mark Jarrell from the
University of Cincinnati. This work was supported by the NSF and
enabled by computational resources of the Center for Computational
Sciences at Oak Ridge National Laboratory, and was a user project
at the CNMS.

The
different contributions to the pairing interaction Vd that leads
to superconductivity in the 2D Hubbard model of the high-temperature
superconductors. The dominant contribution comes from antiferromagnetic
spin fluctuations, while the charge and other fluctuations act
to weaken the pairing interaction.